Need Help w/ Derivates

Drop Calculus

Keep Trying

I'm having a really hard time grabbing a hold of this definition of a derivative concept.

I know that the derivative of [tex]X-X^2 = 1-2X. [/tex], when solving w/ the power rule.
But, I get really lost when I need to solve it using the definition of the derivitave. Can someone please explain to me how I get from the 1st step to the 2nd.

[tex]F(X) = X - X^2 [/tex]

1. [tex]F'(X) = \frac{F(X+H) - F(X)}{H}[/tex]

2. [tex]= \frac{(X+H)^2 - X^2}{H}[/tex]

The way I tried it, I just input [tex]X - X^2 [/tex] for X and I got [tex] (X - X^2 + H) - (X-X^2) [/tex]

Reading your first post, I'll try to clarify what I think is your problem. If you have [tex]f(x)=x^2[/tex], then something like f(2) is easy, right? You just plug in 2 for x and get 4. But what is f(a)? Do the same thing. f(a)=a^2. What is f(x+h) then? Plug in (x+h) for x. f(x+h)=(x+h)^2

You want to solve the limit of [tex] \frac { f(x+h) - f(x)} {h} [/tex] as h approaches 0, right? If f(x) = x - x^2, then f(x+h) - f(x) = (x+h) - (x+h)^2 - (x - x^2)). I'm a little concerned though as these problems you are having are algebraic and not calculus-based, as your thread suggests. Applying basic rules of algebra (up to factoring in the denominator to the expression) should fetch you the right answer.